Theorem simp3i 1142

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp3i	⊢ 𝜒

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp3 1139	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
3	1, 2	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   ∧ w3a 1087

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089

This theorem is referenced by:  hartogslem2  9583  harwdom  9631  divalglem6  16435  structfn  17193  strleun  17194  oppchomfval  17757  sratset  21188  srads  21191  tngip  24666  dfrelog  26607  log2ub  26992  birthdaylem3  26996  birthday  26997  divsqrtsum2  27026  harmonicbnd2  27048  lgslem4  27344  lgscllem  27348  lgsdir2lem2  27370  lgsdir2lem3  27371  mulog2sumlem1  27578  siilem2  30871  h2hva  30993  h2hsm  30994  h2hnm  30995  elunop2  32032  wallispilem3  46082  wallispilem4  46083  prstchomval  49163